Simple Linear Regression:

The estimated intercept is -44850 and the estimated slope is 280.76 for predicting house prices from square feet.To make predictions for inputs in square meters, what slope must you use?


  1. Since the inputs can be converted into square meters i thought the slope would be the same.

  2. In case we change the input( since 1 square foot = .092903 square meter) I multiplied the slope with that number. Both doesnt seem to work out.

Can anyone suggest me where am I going wrong? Thanks in advance.


1 Answer 1


To start off, why would you expect the slope to stay the same if you adjust the scale of your independent variable (price per square feet)? If you divide your x variable by 10, your beta estimate will be multiplied by 10 to compensate for the change and still predict the same y value.

Why is this? Your beta estimate is found by $\beta = \frac{Y - \alpha}{x}$. If $\alpha$ and $y$ stay the same and you make $x$ ten time smaller, $\beta$ would be ten times larger.

Your beta estimate for predicting house prices is 280.76 per square feet. 1 square foot = .092903 square meter so we multiply 280.76 * 1 / (.092903) = 3022.077 per square meter. Intuitively this make sense, we know square meter is a bigger unit of area than square foot, thus we would expect the beta estimate to be higher.


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